Properties

Label 540.4.i
Level $540$
Weight $4$
Character orbit 540.i
Rep. character $\chi_{540}(181,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $3$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 540.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(432\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(540, [\chi])\).

Total New Old
Modular forms 684 24 660
Cusp forms 612 24 588
Eisenstein series 72 0 72

Trace form

\( 24 q + 10 q^{5} + 12 q^{7} + O(q^{10}) \) \( 24 q + 10 q^{5} + 12 q^{7} + 54 q^{11} - 24 q^{13} - 348 q^{17} - 60 q^{19} + 84 q^{23} - 300 q^{25} + 342 q^{29} - 60 q^{31} - 280 q^{35} + 336 q^{37} + 804 q^{41} - 258 q^{43} + 276 q^{47} - 630 q^{49} - 3432 q^{53} + 630 q^{59} + 822 q^{61} + 200 q^{65} - 186 q^{67} + 216 q^{71} - 1500 q^{73} + 96 q^{77} - 888 q^{79} - 228 q^{83} - 360 q^{85} - 828 q^{89} + 24 q^{91} - 520 q^{95} - 546 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(540, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
540.4.i.a 540.i 9.c $2$ $31.861$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-5\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q-5\zeta_{6}q^{5}+(7-7\zeta_{6})q^{7}+(-30+30\zeta_{6})q^{11}+\cdots\)
540.4.i.b 540.i 9.c $8$ $31.861$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(-20\) \(13\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-5-5\beta _{4})q^{5}+(2\beta _{2}-3\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
540.4.i.c 540.i 9.c $14$ $31.861$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(35\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(5-5\beta _{7})q^{5}+(-\beta _{7}-\beta _{9})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(540, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)